I'm installing new speakers in the boat. I noticed the old speakers had 16gauge monster speaker cable running from the head unit and then the monster cable was attached to a thin wire and the thin wire was attached to the speakers. Is this right? should I just plug the new speakers right into the thin wires?

If you have enough of the 16 guage wire to get to your speakers then use this instead of using the smaller guage. What probly happened was whoever installed the previous speakers used the wires that came with the speakers with the connectors on them. If your only running deck power though you'll be fine doing it the way it was done before.